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Multipeakons and the classical moment problem. (English) Zbl 0968.35008

We bring the short and corrected author’s abstract: Classical results of Stieltjes are used to obtain explicit formulas for the peacon-antipeacon solutions of the Camassa-Holm equation. The closed form solution is expressed in terms of the orthogonal polynomials of the related classical moment problem. It is shown that collisions occur only in peacon-antipeacon pairs, and the details of the collisions are analyzed using results from the moment problem. A sharp result on the steepening of the slope at the time of collision is given. Asymptotic formulas are given and the scattering shifts are calculated explicity.

MSC:

35A20 Analyticity in context of PDEs
35C05 Solutions to PDEs in closed form
35L25 Higher-order hyperbolic equations
35Q53 KdV equations (Korteweg-de Vries equations)
44A60 Moment problems
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References:

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